The Martin curve is a power law used by oceanographers to describe the export to the ocean floor of particulate organic carbon (POC). The curve is controlled with two parameters: the reference depth in the water column, and a remineralisation parameter which is a measure of the rate at which the vertical flux of POC attenuates. It is named after the American oceanographer John Martin.
The Martin Curve has been used in the study of ocean carbon cycling and has contributed to understanding the role of the ocean in regulating atmospheric levels.
Background
The dynamics of the particulate organic carbon (POC) pool in the ocean are central to the marine carbon cycle. POC is the link between surface primary production, the deep ocean, and marine sediments. The rate at which POC is degraded in the dark ocean can impact atmospheric CO2 concentration.
The biological carbon pump (BCP) is a crucial mechanism by which atmospheric CO2 is taken up by the ocean and transported to the ocean interior. Without the BCP, the pre-industrial atmospheric CO2 concentration (~280 ppm) would have risen to ~460 ppm. At present, the particulate organic carbon (POC) flux from the surface layer of the ocean to the ocean interior has been estimated to be 4–13 Pg-C year−1. To evaluate the efficiency of the BCP, it is necessary to quantify the vertical attenuation of the POC flux with depth because the deeper that POC is transported, the longer the CO2 will be isolated from the atmosphere. Thus, an increase in the efficiency of the BCP has the potential to cause an increase of ocean carbon sequestration of atmospheric CO2 that would result in a negative feedback on global warming. Different researchers have investigated the vertical attenuation of the POC flux since the 1980s.
In 1987, Martin et al. proposed the following power law function to describe the POC flux attenuation:
(1)
where z is water depth (m), and Fz and F100 are the POC fluxes at depths of z metres and 100 metres respectively. Although other functions, such as an exponential curve, have also been proposed and validated, this power law function, commonly known as the "Martin curve", has been used very frequently in discussions of the BCP. The exponent b in this equation has been used as an index of BCP efficiency: the larger the exponent b, the higher the vertical attenuation rate of the POC flux and the lower the BCP efficiency. Moreover, numerical simulations have shown that a change in the value of b would significantly change the atmospheric CO2 concentration.
Subsequently, other researchers have derived alternative remineralization profiles from assumptions about particle degradability and sinking speed. However, the Martin curve has become ubiquitous as the model that assumes slower-sinking and/or labile organic matter is preferentially depleted near the surface causing increasing sinking speed and/or remineralization timescale with depth.
The Martin curve can be expressed in a slightly more general way as:
where fp(z) is the fraction of the flux of particulate organic matter from a productive layer near the surface sinking through the depth horizon z [m], Cp [mb] is a scaling coefficient, and b is a nondimensional exponent controlling how fp decreases with depth. The equation is often normalised to a reference depth zo but this parameter can be readily absorbed into Cp.
Vertical attenuation rate
The vertical attenuation rate of the POC flux is very dependent on the sinking velocity and decomposition rate of POC in the water column. Because POC is labile and has little negative buoyancy, it must be aggregated with relatively heavy materials called ballast to settle gravitationally in the ocean. Materials that may serve as ballast include biogenic opal (hereinafter "opal"), CaCO3, and aluminosilicates. In 1993, Ittekkot hypothesized that the drastic decrease from ~280 to ~200 ppm of atmospheric CO2 that occurred during the last glacial maximum was caused by an increase of the input of aeolian dust (aluminosilicate ballast) to the ocean, which strengthened the BCP. In 2002, Klaas and Archer , as well as Francois et al. who compiled and analyzed global sediment trap data, suggested that CaCO3, which has the largest density among possible ballast minerals, is globally the most important and effective facilitator of vertical POC transport, because the transfer efficiency (the ratio of the POC flux in the deep sea to that at the bottom of the surface mixed layer) is higher in subtropical and tropical areas where CaCO3 is a major component of marine snow.